class Vector
  def norm
    Math.sqrt(inject(0) { |sum, value| sum += value * value; sum })
  end
end

a = Matrix[[8.04, 2, 0, 0],
           [2, 8.04, 2, 0],
           [0, 2, 8.04, 2],
           [0, 0, 2, 8.04]]

e = Matrix.diagonal(1, 1, 1, 1)

x = Vector[1,1,1,1]
lam = 6

i = @options[:limit].times do |i|
  temp = a - lam * e

  y = temp.inverse * x

  x_old = x

  x = y / y.norm

  lam_old = lam

  lam = (temp * x).zip(x).inject(0) { |sum, (a,b)| sum += a*b; sum }

  break i if (x - x_old).norm <= @options[:epsilon] or (lam - lam_old).abs <= @options[:epsilon]

  x = -1 * x if (x - x_old).norm > 1.99 and (x - x_old).norm < 2.01
end

p "Finished in #{i} iterations", x.to_a.flatten, lam